Given that David has one listing in the Domesday book, and only one
apparently, it would appear that the rest of the Faux male line was
doing something else and not listed in the book. Given the English
inheritance customs (laws?), the eldest son got everything and the rest
- either nothing or something else not land. Where did these "others"
go and what did they do for a living? Did they do to the cities and
become the butcher, baker and candlestick maker? Did they live on the
land and work it?

I know what they did eventually - they came to America where land was
free for the homesteading - but that wasn't until 500 years later, or
thereabouts.

Was Faux a "last name" or was it a place name that eventually became a
last name? If it was a "last name " (don't know when that began in
England/Wales) then it might be less likely to be "taken" by the
"sharecroppers" that a place name, "Hello, I'm Jim of Faux."

Doing some simple math and making some probably way too simple
assumptions, here are some expected descendent rates for this Faux in
the Domesday book, assuming that he was the only Faux (i.e. he had no
living brothers or other male descendents - which is probably hugely
incorrect). Assuming 12 births per generation - 50% living to adulthood
and of those, 50% boys for 3 males per generation that live to
procreate. A generation is 25 years for this calculation. Multiplying
this out, we have 22 generations to 1591 when the first English began
coming to the colonies. Given this assumption of 3 living males per
generation, we have an astounding 31,381,059,609 males in the final
generation of 1591, any of all of which could have migrated to the US -
and all from that 1 person in 1066.

Redoing the math with an assumption of 2 living males per generation
gives us 4,194,304 individuals in the 1591 generation. An assumption of
1.5 living (yes I know, half a person can't live - but it's a math thing
- an average) gives us 7,482.

Having done all of this - given the English rule of land descendency -
only 1 of those above people, however many there were would own the
orginal Faux land from the Domesday book. What did the rest of all of
those people do and where did they go? What name did they use? Did
they still use Faux if they went elsewhere and weren't landed? We can't
test them if we can't find them.